Analytical Solutions to the Navier-Stokes Equations

TL;DR

This paper develops analytical solutions for the isothermal and pressureless Navier-Stokes equations with density-dependent viscosity, extending previous Euler-Poisson solutions to a broader class of fluid dynamics models.

Contribution

It introduces a new family of analytical solutions for specific Navier-Stokes equations, expanding the understanding of their solution structures.

Findings

Constructed analytical solutions for isothermal Navier-Stokes equations.

Extended solutions to pressureless Navier-Stokes equations with density-dependent viscosity.

Demonstrated the applicability of solution structures from Euler-Poisson equations to Navier-Stokes models.

Abstract

With the previous results for the analytical blowup solutions of the N-dimensional Euler-Poisson equations, we extend the similar structure to construct an analytical family of solutions for the isothermal Navier-Stokes equations and pressureless Navier-Stokes equations with density-dependent viscosity.